Just what is it that makes today’s math so different, so appealing?

It’s no surprise that last year, Williams College turned out more than five times the national average of math majors, and that this year 43 more seniors plan to join their ranks.Williams math professors have been known to do anything to capture their students’ attention and hold onto it until they succeed in communicating a critical message: math is exciting.

“It’s the ultimate structure of reality,” said Tom Garrity, mathematics department chair, who spent time in Math 301 last Thursday discussing the Fundamental Theorem of Calculus and genetically mutated sea bass, among other things. “Math is not a spectator sport,” Garrity said. “Most people fall asleep while they’re listening to math. I do.”

But no one fell asleep that day in class. Garrity repeatedly swung a lengthy wooden ruler over his head during class, smacking it against his desk at opportune moments. “Oh, sorry,” he said the first time. “It slipped.”

The lecture of the day focused on a proof of the famous Fundamental Theorem. “We’re going to state what it is,” he said, “and then prove it rigorously.”

Over the course of the next hour and fifteen minutes, Garrity darted around the classroom and jabbed at the chalkboard in quick movements. “I know this is really fast,” he said at one point, scribbling furiously on the board. “[I’m] keeping math a closed society, keeping my job safe.”

Garrity’s humor kept students alert, and his spoken challenge kept them sharp. Soon it was the students’ turn to participate; several were quick to point out when a constant in his equation turned inexplicably from a three into a seven.

“That’s the mistake of a doofus,” Garrity said as he corrected the error.

Humor also a key component for other faculty in reaching students. “Mel Slugbate,” known across the nation since he appeared in Newsweek magazine in June of 2000 and in last year’s Abercrombie and Fitch winter catalogue, is the creation of another math professor. Colin Adams dons Slugbate’s plaid suit and thick glasses on occasions when describing the space in a hyperbolic three-manifold could best be accomplished by a real-estate salesman.

For Adams, the tacky character is a means to reaching students. “My goal is: I want people to see the beauty in mathematics. And any way I can keep their attention long enough for them to see the beauty of mathematics, I’m happy to do it.”

He added, “The scary part is, he [Mel] gets more invitations to speak than I do.”

Faculty members in the math department are accomplished outside of their performance abilities. This year, Edward Burger received the Mathematical Association of America Deborah and Frank Tepper Haimo National Award for Distinguished College or University Teaching of Mathematics. Only 30 of these awards, which are granted to the nation’s best college and university math professors, have been given since the award’s inception, and two others went to Williams faculty as well. Adams and Professor Frank Morgan were recipients in past years.

Of the department’s success, Adams said, “It comes from an ethos in the department of how important teaching is to all of us, and I fully expect that there will be other members of the department that will win in the future.”

Math faculty at other colleges are taking note. Ted Vessey, a professor at St. Olaf College in Minnesota, is conducting research on various undergraduate mathematical programs.

“I am particularly interested in those schools where there is a surprisingly large number of math majors,” he said. “When I was at Middlebury, a friend there said that I just had to visit Williams.” Vessey spent time in October evaluating the department and found the curriculum, facilities, student enthusiasm, and faculty activity to be excellent. “I have not visited a large number of schools,” he said, “but of those I have, I would rate Williams’ department as one of the finest I have seen.”

Vessey was impressed with the energy of the math faculty. “The department has a surprising level of professional activity for a liberal arts college, even to [the extent of] hosting a meeting of the research-dominated American Mathematical Society this fall.”

Math majors also laud their professors. “They are personable and intelligent, amusing, and exceptionally competent,” said Brian Katz ’03.

Eileen Bevis ’03 cited their enthusiasm for all levels of mathematic discourse. “These are world-class mathematicians. . .they’re teaching lower-level math classes, and they’re still excited.”

Topher Goggin ’02 has another idea of what makes the math faculty unique. “What I’ve really found sets the math department apart is the out-of-class interaction between faculty and students,” he said. Three professors have participated in Goggin’s radio show. “In general, they’re just a fun, funny group of people who also happen to have some great quirks for exploitation on the radio.”

In addition to attending weekly colloquia followed by snacks and monthly math department dinners, members of the faculty organize conferences, apply for grants, research topics of interest, write and contribute to textbooks, participate with students in contests, and run summer programs.

The SMALL Undergraduate Research Project is a summer program that allows groups of students to conduct research on a focused area of math with members of the faculty.

“SMALL is an intense and exciting experience,” said Cesar Silva, professor of mathematics. The nine-week program is an opportunity for students to gain an in-depth knowledge of a particular subject; in some cases, students publish their work in mathematics journals.

“A paper I’m finishing up now is certainly a collaboration of two summers’ worth of SMALL students,” said Garrity. “They do great work.” Adams taught a course on hyperbolic three-manifolds and shared the work of his four students with an audience in Korea.

“SMALL is organized in groups, each with about four students and a faculty advisor,” said Silva. Students who are invited to participate live in Agard; of the maximum 18 students, about half come from other schools.

“Last year, there were over 140 applications for the nine positions we offered to outside students,” Silva explained. “SMALL is the largest undergraduate mathematics summer research program in the country, with the largest group of in-house students”.

Last summer’s work culminated with a trip to Madison, Wis. for the annual meeting of the Mathematical Association of America, where students presented the results of their research.

Eric Schoenfeld ’03 participated in SMALL under the guidance of Morgan. “We were studying soap bubbles,” he said. Schoenfeld and his group travelled to the University of California at Berkley for three weeks to deliver talks on their research at the Mathematical Sciences Research Institute.

“The problem is to find the least-perimeter way to enclose and separate two areas,” he explained. In addition to working in a corner office on a hill overlooking the Bay area, Schoenfeld said, “We got to meet some really accomplished mathematicians and hang out in the city and do math.”

The fruits of this group’s efforts will not be forgotten any time soon. “My group and I will probably be publishing a couple papers over the next year from research we did this summer,” said Schoenfeld. “It’s our research, and that kind of opportunity is rare, I think.”

Schoenfeld emphasized that working with Morgan, who has held positions at, among other institutions, MIT, Stanford, and Princeton, was an experience that math majors at the College are lucky to have. “He’s giving undergrads like me a chance to work with him and some other amazing mathematicians,” he said. “It’s really pretty cool.”

Of all the activity in the math department, Adams said, “That creates some critical mass of energy and excitement, and I think that really helps to make students feel like it’s a community of people all interested in mathematics.”

Most math majors are converts to the department, won over by the enthusiastic professors and constant activity. “I did not originally plan to major in math,” said Goggin. “It just sort of happened. I just kept on taking classes and ended up picking it up as a major.” Bevis expressed similar sentiments. “It catches on,” she said.

Katz predicted a promising future for the department: “The reputation and recent press on the department have led to more students coming to this school to be math majors, which only raises the bar.”

Meanwhile, in the flurry of excitement, the core remains the classroom dynamic: what occurs there is fundamental. “Are we doing anything interesting today?” a student asked Garrity last Thursday before class. “Yes,” he answered without hesitation. “Secrets of the universe.”